Initial Plus/Minus Numbers for the '97 Season

I've been silent for a few weeks, working on a bigger project, and the fruits of that labor are appearing. A few months ago, the NBA released play-by-play dating going back to the 1996-97 season, allowing for the possibility of more advanced basketball stats beyond the typical box score counting stats. NBA.com already lists detailed player shooting data (percentages and totals by distance), but the Holy Grail was plus/minus -- it had become the most respected advanced stat out there, beating out other metrics in future, out of sample predictions, especially even further into the future when more guys move from team to team.

When no one stepped up to the plate to break down the play-by-play data, I decided to do this myself. The problem was the data only included last names, making it difficult to discern exactly who was on the court. However, home and away teams have separate columns, so the problem is reduced to only teams where two players have the same name. There are 6 such teams: Portland with Rumeal and Cliff Robinson; New York with Buck and Herb Williams; New Jersey with another set of Williams's, in Jayson and Reggie; Phoenix with Mike and Chucky Brown (no, not that Mike Brown); Denver with LaPhonso and Dale Ellis, as well as Brooks and LaSalle Thompson; and Indiana with Dale and Antonio Davis. Fortunately, the Brown's never played in the same game, so they were easily separated. The rest of the player pairs were successfully separated with the exception of the Davis brothers, who are similar anyway, and the Ellis's, who remain the largest problem. For the matchup file, I combined the pairs as one player; and as such, the initial results below should be taken with a grain of salt, though mostly for players on those two teams (Denver and Indiana.)

Without further ado, here's a table of the top players for 1996-96 by adjusted plus/minus including the playoffs with a minutes cut-off of 250:

Rank	Player....................	Adj. +/-	St. Err.	Minutes	PER	WP/48
1	Mookie Blaylock	15.79	7.01	3056	20.4	0.197
2	Tim Hardaway	15.64	6.79	3136	20.8	0.198
3	Michael Jordan	13.92	5.48	3106	27.8	0.283
4	Latrell Sprewell	13.13	6.79	3353	19.7	0.115
5	Patrick Ewing	13.08	5.78	2887	21.3	0.163
6	Terry Mills	12.92	5.82	1997	16.4	0.148
7	Hakeem Olajuwon	12.81	6.46	2852	22.7	0.154
8	Greg Anthony	12.81	7.75	1863	16.6	0.090
9	Kevin Garnett	12.49	5.87	2995	18.2	0.116
10	John Stockton	12.07	16.05	2896	22.1	0.226
11	Tyrone Hill	11.79	6.82	2582	17.8	0.184
12	Mitch Richmond	10.94	6.38	3125	21.6	0.166
13	Stanley Roberts	10.80	8.94	378	14.1	0.060
14	Melvin Booker	10.65	9.31	430	8.8	0.014
15	Shaquille O'Neal	10.62	5.88	1941	27.1	0.197
16	Gary Payton	10.52	6.74	3213	21.8	0.193
17	Nate McMillan	10.28	6.41	798	14.1	0.158
18	Alonzo Mourning	9.87	5.38	2320	21.6	0.174
19	Litterial Green	9.77	10.10	311	13.5	0.119
20	Jerome Kersey	9.70	4.95	1766	12.3	0.102

*Per 200 possessions (roughly a full game)

**This is the entire '97 season plus the playoffs with the exception of 11 missing games.

***Players with under 250 minutes were combined into one variable. That coefficient, by the way, was -5.94 with a st. error of 7.14.
****Playoff possessions are weighted twice as much (i.e. they're twice as important as regular season ones.)

The important thing to note about adjusted plus/minus data is that the estimates are not precise: there are usually huge ranges for the predictions. The standard errors for the guys in the top 20 table are around 5 to 8, meaning Ewing, for example, isn't significantly "better" than Mourning (by adj. +/-.) With such high variation, what use are these results? For one, it's more evidence to use in evaluation of historical (and even some current) players. One year plus/minus is a little wacky, but once you're armed with a few years of data and better techniques like ridge regression you can find patterns and judge which players have consistently high, or mediocre, impact. For wacky results, you may have noticed three non-entities in the top 20: Stanley Roberts (Shaq's former teammate from LSU), Melvin Booker, and Litterial Green. That's pretty normal in one year adjusted plus/minus, as it's the biggest weakness (low minute guys.) As a sanity check, homecourt advantage was calculated as +3.29.

If you're wondering how a certain star ranked, I put the most notable guys in the table below:

Rank	Player....................	Adj. +/-	St. Err.	Minutes	PER	WP/48
22	Christian Laettner	9.36	6.38	3140	19.1	0.177
23	Scottie Pippen	9.28	5.42	3095	21.3	0.203
25	Horace Grant	8.82	5.41	2496	17.3	0.148
27	Kendall Gill	7.69	5.75	3199	19.6	0.132
31	Vlade Divac	7.44	6.68	2840	17.9	0.123
33	Chris Webber	7.12	5.77	2806	21.8	0.159
37	Hersey Hawkins	6.68	5.95	2755	17.6	0.190
47	Detlef Schrempf	5.56	5.43	2192	18.3	0.174
48	Clyde Drexler	5.54	5.94	2271	19.9	0.172
51	Rasheed Wallace	5.38	5.63	1892	18.4	0.163
52	Anfernee Hardaway	5.15	5.54	2221	21.4	0.175
54	Jeff Hornacek	5.06	7.58	2592	18.8	0.190
55	Sam Cassell	4.98	5.40	1714	18.4	0.108
56	Jason Kidd	4.91	4.89	1964	16.9	0.107
58	Karl Malone	4.76	8.60	2998	28.9	0.268
70	Derrick Coleman	4.33	5.63	2102	17.3	0.076
77	Kenny Anderson	3.94	6.73	3081	19.5	0.193
79	Toni Kukoc	3.90	4.91	1610	20.2	0.204
80	Reggie Miller	3.76	6.89	2966	20.2	0.200
82	Dikembe Mutombo	3.54	6.76	2973	19.0	0.183
94	Kevin Johnson	3.22	3.22	2658	22.9	0.211
95	Eddie Jones	3.07	3.07	2998	17.3	0.154
100	Allen Iverson	2.94	2.94	3045	18.0	0.065
108	Grant Hill	2.32	2.32	3147	25.5	0.223
113	Vin Baker	2.23	2.23	3159	20.1	0.127
122	Arvydas Sabonis	1.97	1.97	1762	21.8	0.205
141	Kobe Bryant	0.27	5.24	1103	14.4	0.079
160	Dennis Rodman	-0.76	5.20	1947	13.9	0.148
173	Shawn Kemp	-1.48	5.64	2750	20.7	0.174
197	Anthony Mason	-2.30	6.52	3143	18.9	0.173
214	Rik Smits	-2.93	5.24	1518	18.3	0.105
222	Damon Stoudamire	-3.22	6.59	3311	18.1	0.110
252	Terrell Brandon	-4.84	6.58	2868	21.5	0.181
256	Chris Mullin	-5.24	5.82	2733	17.6	0.124
273	Rony Seikaly	-6.49	5.66	2615	18.3	0.125
275	Tom Gugliotta	-6.52	6.37	3131	19.0	0.103
284	Dominique Wilkins	-6.96	5.43	1945	19.6	0.083
288	Rod Strickland	-7.21	9.72	2997	19.7	0.141
324	Shareef Abdur-Rahim	-10.45	5.88	2802	17.4	0.049

Non-traditional stars like Hornacek and Pippen rate well by this metric. It's disappointing to see Grant Hill, whose prime was cut short, and Sabonis with just decent numbers. I was hoping they'd have monster impact. It's interesting to see who doesn't fare well, however -- the old star Wilkins is a net negative, Kemp is as well, and a young Shareef Abdur-Rahim, often called a guy who put up good stats on a bad team, brings up the rear. I am surprised, however, by Dennis Rodman's low ranking. This is Rodman the Rebounder on his second title run, although his numbers weren't great in the playoffs. It's shocking to see Malone so low given his MVP, but both he and Stockton has high standard errors, suggesting there were problems untangling the two guys since they both never missed a game.

Remember that one year adjusted plus/minus stats are volatile. It's normal to see a guy in his prime with a terrible +/- one season and then rebound with an excellent one next season. If the roster rotations were rigid, it's impossible for this method to pick up on which guy actually deserves the credit on the court. With another year of data behind it, the plus/minus stats (prior-informed with RAPM or two year adj. +/-) will improve by a large margin. RAPM deals better with low minute guys, which can change some of the numbers completely like a really complicated maze of dominoes.

And why did I set a minutes requirement of 250 for the tables? The weakness of plain adjusted plus/minus is that it dumbly guesses absurd estimates with guys who have few minutes. For example, without a minutes cutoff you get results like Evric Gray with an earth-shattering +27.2 ... in 42 minutes all season. Gary Grant and Jack Haley were another two guys ranked above legends like Olajuwon, though David Robinson was +14.6 in 147 minutes. Since they have so few possessions, these low minutes guys are basically play-doh to fill in any cracks to minimize the squared error. This is where ridge-regression (RAPM) excels: a heavy dose of regression to the mean (or prior.) If you're going to have a high rating, you'd better prove it with many possessions or a high rating the previous year.

I'll clean up the data more and tackle RAPM further, but for now some initial results were worth posting.

Edit: I used Rosembaum's preferred minutes cutoff of 250. Before I was using something really low.
Second edit: found some problems with how the name for the player pairs were being assigned, plus I eliminated all but two player pairs (hence the label "initial" results.) As a result the numbers are completely revamped.